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{{short description|One of two formulae that are used in the resolution of Diophantine equations}} ...tity''' refers to one of two formulae that are used in the resolution of [[Diophantine equation]]s. ...

...H. | last2=Silverman | authorlink2=Joseph H. Silverman | title=Diophantine Geometry: An Introduction | series=[[Graduate Texts in Mathematics]] | volume=201 | ...st=Serge | last=Lang | authorlink=Serge Lang | title=Survey of Diophantine Geometry | publisher=[[Springer-Verlag]] | year=1997 | isbn=3-540-61223-8 | zbl=0869 ...

...H. | last2=Silverman | authorlink2=Joseph H. Silverman | title=Diophantine Geometry: An Introduction | series=[[Graduate Texts in Mathematics]] | volume=201 | ...st=Serge | last=Lang | authorlink=Serge Lang | title=Survey of Diophantine Geometry | publisher=[[Springer-Verlag]] | year=1997 | isbn=3-540-61223-8 | zbl=0869 ...

==Diophantine dimension== ...''&nbsp;>&nbsp; ''d''^''k''. Algebraically closed fields are of Diophantine dimension 0; [[quasi-algebraically closed field]]s of dimension 1.<ref name ...

...in [[Diophantine approximation]], [[Diophantine equation]]s, [[arithmetic geometry]], and [[mathematical logic]]. ...algebraic variety, let <math>D</math> be an effective [[divisor (algebraic geometry)|divisor]] on <math>X</math> with at worst normal crossings, let <math>H</m ...

...curve]]s that generalizes the [[Manin-Mumford conjecture]] in [[arithmetic geometry]]. The conjecture was proven by [[Emmanuel Ullmo]] and [[Shou-Wu Zhang]] in ...geometry. Bellairs workshop in number theory, tropical and non-Archimedean geometry, Bellairs Research Institute, Holetown, Barbados, USA, May 6–13, 2011 | zbl ...

In [[mathematics]], in [[Diophantine geometry]], the '''conductor of an abelian variety''' defined over a [[local field|l ...ook | author=S. Lang | authorlink=Serge Lang | title=Survey of Diophantine geometry | url=https://archive.org/details/surveydiophantin00lang_347 | url-access=l ...

In mathematics, '''Minkowski's second theorem''' is a result in the [[geometry of numbers]] about the values taken by a [[Normed vector space|norm]] on a .... | last=Cassels | author-link=J. W. S. Cassels | title=An introduction to Diophantine approximation | series=Cambridge Tracts in Mathematics and Mathematical Phy ...

...[[Markov number|Markov Diophantine equations]] and also in the theory of [[Diophantine approximation]]. Starting from [[Hurwitz's theorem (number theory)|Hurwitz's theorem]] on Diophantine approximation, that any real number <math>\xi</math> has a sequence of rati ...

...r>[[Bombieri–Lang conjecture]]<br>[[Glossary of arithmetic and diophantine geometry#M|Mordell–Lang conjecture]] ...y [[Louis Mordell]] in 1922. It is a foundational theorem of [[Diophantine geometry]] and the [[arithmetic of abelian varieties]]. ...

{{short description|Book on the geometry of numbers}} ...a book on the [[geometry of numbers]], an area of mathematics in which the geometry of [[Lattice (group)|lattices]], repeating sets of points in the plane or h ...

The [[Diophantine problem]] of finding integer points on a superelliptic curve can be solved ...H. | last2=Silverman | authorlink2=Joseph H. Silverman | title=Diophantine Geometry: An Introduction | series=[[Graduate Texts in Mathematics]] | publisher=[[S ...

| thesis_title = Some Aspects of Diophantine Approximation | known_for = [[Number theory]]<br>[[Diophantine equations]]<br>[[Baker's theorem]]<br>[[Stark–Heegner theorem|Baker–Heegner ...

...analogous to a line. Arithmetic surfaces arise naturally in [[diophantine geometry]], when an [[algebraic curve]] defined over ''K'' is thought of as having r ...d surface over a Dedekind scheme of dimension one.<ref>Liu, Q. ''Algebraic geometry and arithmetic curves''. Oxford University Press, 2002, chapter 8.</ref> Th ...

...ame=Dickson>Dickson, L. E., ''History of the Theory of Numbers, Volume II: Diophantine Analysis'', Chelsea Publ. Co., 1952, pp. 688–691.</ref> ...g both sides by ''abc'' shows that the optic equation is equivalent to a [[Diophantine equation]] (a [[polynomial equation]] in multiple integer variables). ...

...Italian mathematician, specializing in [[number theory]] and [[Diophantine geometry]]. ...ità IUAV di Venezia]]. From 2003 to the present he has been a Professor in Geometry at the Scuola Normale Superiore di Pisa.<ref name=CV>[https://web.archive.o ...

[[Category:Arithmetic problems of plane geometry]] [[Category:Triangle geometry]] ...

...ael Liam McQuillan''' is a Scottish [[mathematician]] studying [[algebraic geometry]]. As of 2019 he is Professor at the [[University of Rome Tor Vergata]]. ...i-dense).<ref>{{cite journal | last=McQuillan | first=Michael Liam | title=Diophantine approximations and foliations | journal= [[Publications Mathématiques de l' ...

...''' is a far-reaching generalisation of many famous [[Diophantine geometry|Diophantine]] conjectures and statements, such as [[André–Oort conjecture|André–Oort]], ...first=John | editor2-link=John Tate (mathematician) | title=Arithmetic and geometry. Papers dedicated to I. R. Shafarevich on the occasion of his sixtieth birt ...

...totally different methods which has many applications in modern arithmetic geometry. ...plicity estimates a further new ingredient was a very sophisticated use of geometry of numbers to obtain very sharp lower bounds. ...